Quartic-Scaling Analytical Energy Gradient of Scaled Opposite-Spin Second-Order Møller−Plesset Perturbation Theory

The analytical gradient of the "scaled opposite spin" (SOS-) and "modified opposite spin" (MOS-) second-order Møller-Plesset perturbation theory (MP2) methods is derived and implemented. Both energy and the first derivative can be evaluated efficiently with a fourth-order scaling algorithm by using a combination of auxiliary basis expansions and Laplace transformation techniques as opposed to the traditional fifth-order approach of MP2. A statistical analysis of 178 small molecules suggests that the new gradient scheme provides geometries of MP2 quality, indicating the reliability of the method in general chemical applications. A more specific study of the group VI transition metal carbonyl complexes indicates that the new scheme improves the MP2 description relative to available experimental data and higher-order theories. The proposed gradient scheme thus endeavors to obtain improved structural features at reduced computational cost.